Question

find the area of the shaded region in the figure. use the $pi$ key for $pi$. the area of the shaded region in the figure is approximately $square$ $ft^{2}$ (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Find area of the circle

The formula for the area of a circle is $A_{circle}=\pi r^{2}$. Given the diameter of the circle is $6.7$, the radius $r = \frac{6.7}{2}=3.35$. So $A_{circle}=\pi\times(3.35)^{2}=\pi\times 11.2225$.

Step2: Find area of the square

The formula for the area of a square is $A_{square}=s^{2}$, where $s = 1.5$. So $A_{square}=(1.5)^{2}=2.25$.

Step3: Find area of the shaded region

The area of the shaded region $A = A_{circle}-A_{square}=\pi\times11.2225 - 2.25$. Using $\pi$ key on calculator, $A\approx11.2225\pi- 2.25\approx11.2225\times3.14 - 2.25=35.04865-2.25 = 32.8$.

Answer:

$32.8$